Topology of Discriminants and Their Complements

Victor A. Vassiliev
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Victor A. Vassiliev: Independent University of Moscow

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 209-226 from Springer

Abstract: Abstract The general notion of a discriminant is as follows. Consider any function space $$\mathcal{F}$$ ℱ , finite dimensional or not, and some class of singularities S that the functions from $$\mathcal{F}$$ ℱ can take at the points of the issue manifold. The corresponding discriminant variety ∑(S) ⊂ $$\mathcal{F}$$ ℱ is the space of all functions that have such singular points. For example, let $$\mathcal{F}$$ ℱ be the space of (real or complex) polynomials of the form 1 $${x^d} + {a_1}{x^{d - 1}} + \cdots + {a^{d,}}$$ x d + a 1 x d − 1 + ⋯ + a d , and S = {a multiple root}.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_16

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